1. Introduction

Data visualization refers to the techniques used to communicate data or information by encoding it as visual objects (e.g., points, lines or bars) contained in graphics. According to Friedman (2008) the main goal of data visualization is to communicate information clearly and effectively through graphical means.

According to Friedman, that does not mean that data visualization needs to look boring to be functional or extremely sophisticated to look beautiful. To convey ideas effectively, both aesthetic form and functionality need to go hand in hand. However, designers often fail to achieve a balance between form and function, creating gorgeous data visualizations which fail to serve their main purpose, communicate information (Friedman 2008).

Key concept
Graphs are a great tool to explore the data and they are essential for presenting results. Their main goal is to communicate information clearly and efficiently to users. It is one of the steps in data analysis or data science.

Each new visualization can give us insights about our data. Some of this revealing information may already be known (but perhaps not yet demonstrated), while other aspects may be completely new to us. The figure below represents the process of searching new perceptions in the data (Aisch 2019).

P2 Learning outcomes

  • Learn the grammar of graphics of ggplot2

  • Create the most common bioinformatic graphs (scatter plots, line plots, bar plots, …)

  • Distinguish graphic quality indicators

    • Integrity
    • Chartjunk
    • Data-ink ratio

  • Learn the characteristics of effective graphic displays

1.1 Practicals organization

In this practical, we are going to use the RStudio integrated development environment (IDE) for R. R is a programming language for statistical computing and graphics.

The current document in which we are working is an R Markdown document. Similar to a Jupyter Notebook, R Markdown documents are fully reproducible and allow you to combine text, images and code –this time, R programming language.

To render a R Markdown document to a HTML file, you just need to click the Knit button that you’ll see in the RStudio bar. This HTML file can be shared as a report.

You don’t need to render the whole document every time you want to see the result of your R code. You can click in the Run current chunk button or use the keyboard shortcut Ctrl+Alt+C and the result of the code will appear below it.

You will see different icons through the document, the meaning of which is:

: additional or useful information
: a worked example
: a practical exercise
: a space to answer the exercise
: a hint to solve an exercise
: a more challenging exercise

2. Tools installation

We strongly recommend using a Linux operating system and get used to work with the terminal. In this practical though, we won’t use it and there’s almost no difference in using Windows RStudio or Linux RStudio.

2.1 Installing R

R programming language can be downloaded from here, and is available for Windows, Linux and macOS.

2.2 Installing RStudio

RStudio is available to download from here. You can easily install it in Windows, Linux and macOS.

2.3 Installing a package

R packages are collections of functions and/or data developed by the community.

To install a package, we use the install.packages() function, indicating between quotes the name of the package we want to install.

2.3.1 Installing ggplot2

ggplot2 is a data visualization package for the statistical programming language R (Wickham 2009). It was created by Hadley Wickham, implementing Leland Wilkinson’s Grammar of Graphics —a general scheme for data visualization which breaks up graphs into semantic components (Wilkinson 2010).

To install the ggplot2 package, use the following:

install.packages("ggplot2")

2.4 Loading a package

To load a package, we use the function library(), indicating the name of the library we want to load.

In the case of ggplot2, you’ll use:

library("ggplot2")

You’re ready to start creating graphs!

3. Quick introduction to R

3.1 Loading data

To load data from a delimited text file, we normally use the read.table() function, indicating the name of the file we want to load (including the directory if the file is not located in the same working directory as the R session). Furthermore, we can specify if the file has a header with header = TRUE (by default FALSE) or the file delimiter with sep = (by default sep = "").

For example, for loading the content of data.txt file, which has a header and it’s a tab-delimited file, we will write:

data <- read.table("data.txt", header = TRUE, sep = "\t")

Also, the read.csv() function allows opening files with a .csv format (comma-separated values data) and the read.xlsx() function of the xlsx package allows opening Microsoft Excel files.

3.2 Data formats

In R, the most common data types are:

  • Character: consist of numbers, letters or words delimited with quotes (e.g. "AGT", "2")
    • Numeric: consists of numbers such as integers (e.g. 1, -3) or doubles (e.g. 0.5, -12.3)
  • Integer: integer numbers, such as 2L (the L tells R to store this as an integer)
  • Logical: logical values can take on one of two values: TRUE, T or FALSE, F

To know the data type, you can use the class() function.

type_list <- list(TRUE, 1.2, 10L, "a")
sapply(type_list, class)
## [1] "logical"   "numeric"   "integer"   "character"

Elements of the previous data types may be combined to form data structures. The main data structures are:

  • Vector: consists of an ordered set of values of the same type and/or class (e.g. numeric, character, date, etc.).
# A vector x of mode numeric
x <- c(1, 2, 3)

# A vector y of mode logical
y <- c(TRUE, TRUE, FALSE, FALSE)

# A vector z of mode character
z <- c("Sarah", "Tracy", "Jon")
  • Matrices: vectors indexed using two indices instead of one.
# A 2 x 2 matrix
matrix22 <- matrix(
  c(1, 2, 3, 4),
  nrow = 2,
  ncol = 2)
  • Factors: a collection of values that all come from a fixed set of possible values. A factor is similar to a vector, except that the values within a factor are limited to a fixed set of possible values.
# A vector containing "dna" and "rna"
factor_vector <- as.factor(c("rna", "dna", "dna", "rna"))
str(factor_vector)
##  Factor w/ 2 levels "dna","rna": 2 1 1 2

Remember to always transform categorical variables to a factor. You can have a categorical variable as characters, like the previous example (“dna” and “rna”) but also as numerical values (you can have groups “1”, “2” and “3”). In this case you need to tell R to use numerical values as a factor, transforming them using the as.factor() function.

  • Lists: a collection of data structures. The components of a list can be of any structure.
# A list
x <- list(1, "a", TRUE, 1+4i)
  • Data.Frame: a collection of vectors that all have the same length. This is like a matrix, except that each column can contain a different data type. The attributes of an object provide specific information about the object itself.
# A dataframe
dat <- data.frame(id = letters[1:10], x = 1:10, y = 11:20)

4. Data visualization theory

There is grounded theory about data visualization (Ortiz 2014). This section highlights the pioneering contribution of the work of Edward Tufte (1942–), American statistician and professor emeritus of political science, statistics, and computer science at Yale University. One of the central ideas of Tufte’s work refers to the removal of non-useful elements in the graphics, as they distract attention from the explanatory elements. He coined the word chartjunk to refer to this useless, non-informative, or information-obscuring elements (Minguillon 2016). In contrast, the concept of excellence was defined as the communication of complex ideas with clarity, precision and efficiency (Minguillon 2016).

4.1 Graphic quality indicators

Applicable to any graphic. These are concrete and relatively objective guides to assess the quality of a graph (Tufte, 2001).

  • Graphical integrity: refers to how accurately the visual elements represent the data. The lie factor, how much a graphic deviates from the actual data, should be minimized.
  • Chartjunk: minimize the use of graphic decoration that interferes with the interpretation of the data: 3D effect, patterns…
  • Data-ink ratio: maximize the data ink vs. total ink used to print the graphic.

4.1.1 Lie factor, chartjunk and pies

The lie factor is the ratio of the size of an effect shown in the graphic to the size of the effect in the data. Ideally, the lie factor should be 1 (no distortion).

A chartjunk is an unnecessary or confusing visual element in graphs and are not necessary to comprehend the information represented on the graph or distract the the viewer from this information.

A popular design that qualifies as chartjunk and introduce lie factors is the 3D pie. In the figure, we can see how segment C looks bigger than B, although is not the case (lie factor). The reason is the variation in the perspective that does not correspond to variation in the data (chartjunk).

If we correct by removing the 3D effect, the lie factor is reduced, but there are still elements that can improve the understanding of the graph: the relation between the colour, the quantification and the category. We can add tags as shown in the series on the right, but then: why not simply show the data in a table? What does the pie graph add to the interpretation? This could be more difficult if, for example, more categories are added.

4.1.2 Data-ink ratio

Maximizing the proportion of data-ink in our graphs has immediate benefits. The rule is: if there is ink that does not represent variation in the data, or the removal of that ink does not represent loss of meaning, that ink must be removed.

\[ Data-ink\;ratio\;=\;\frac{Data-ink}{Total\;ink\;used\;to\;print\;the\;graphic} \] According to the Tufte principle, the data must be displayed above all, so that everything that does not provide information, must be deleted (including background color, borders, grids, …).

4.2 Characteristics of effective graphic displays

As we have previously introduced, Tufte defined the term excellence in data visualization as communicating complex ideas with clarity, precision and efficiency. A good visualization should:

5. The grammar of graphics

In a natural language, there are a series of rules that organize words into sentences, the grammar. Wilkinson (2005), created a grammar of graphics which offers us the basic elements to create them.

The components (or layers) of the grammar of graphics are:

6. First steps with ggplot2

The following examples will walk you through the basic components of the ggplot2 grammar. The examples use data from the datasets package, which is already loaded by default in the R session, as well as some datasets loaded with ggplot2 package. ggplot2 requires data to be stored in data frames and in a tidy format (one observation per row and one variable per column):

head(iris)
##   Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1          5.1         3.5          1.4         0.2  setosa
## 2          4.9         3.0          1.4         0.2  setosa
## 3          4.7         3.2          1.3         0.2  setosa
## 4          4.6         3.1          1.5         0.2  setosa
## 5          5.0         3.6          1.4         0.2  setosa
## 6          5.4         3.9          1.7         0.4  setosa
class(iris)
## [1] "data.frame"

Example 1 | Creating a scatter plot

1a | Basic scatter plot

For the first problem we want to represent the relationship between the variables Sepal.Width and Sepal.Length from the iris data frame. This data frame a collection of data that quantifies the morphologic variation of iris flowers of three related species (setosa, versicolor and virginica).

This famous (Fisher’s or Anderson’s) iris dataset gives the measurements in centimeters of the variables sepal length and width and petal length and width, respectively, for 50 flowers from each of 3 species of iris. You can type ??iris in the R console to read a description of the data.

To represent any graph in ggplot2 we need two basic functions that are combined with a + sign:

ggplot(data = iris, mapping = aes(x = Sepal.Width, y = Sepal.Length)) +
  geom_point()

The variables that we want to represent are wrapped within an aes() function, that specifies the mapping between the variables and the aesthetic attributes (in this case we map them to spatial positions, x and y). We call the variables directly by their names, because we also pass the entire data frame to the call with the data argument, so ggplot knows were to get them from. Finally, we need to add the geometric object we want to represent. In this case, points.

1b | Represent extra variables

Another variable in the data indicates the species (Species) it was measured. There are three species: setosa, versicolor and virginica.

table(iris$Species)
## 
##     setosa versicolor  virginica 
##         50         50         50

Let’s say we want to represent the different types of species in different colours. In this case we want to use Species as a categorical variable, i.e., as a factor. By default, this variable is already a factor:

class(iris$Species)
## [1] "factor"

We use Species in the colour aesthetic:

ggplot(data = iris, mapping = aes(x = Sepal.Width, y = Sepal.Length, colour = Species)) +
  geom_point()

Note that ggplot adds a legend by default for all the variables that have been mapped to some aesthetic attribute. This way we can read all the variables without extra effort.

Exercise

Try mapping Species to another aesthetic attribute instead of colour, such as shape, size, alpha. Are you getting any warning message? Why?

Answer:

Example 2 | Creating a bar plot

For this second exercise we are going to use mtcars dataset, which contain information about the fuel consumption and 10 aspects of automobile design and performance for 32 automobiles.

head(mtcars)
##                    mpg cyl disp  hp drat    wt  qsec vs am gear carb
## Mazda RX4         21.0   6  160 110 3.90 2.620 16.46  0  1    4    4
## Mazda RX4 Wag     21.0   6  160 110 3.90 2.875 17.02  0  1    4    4
## Datsun 710        22.8   4  108  93 3.85 2.320 18.61  1  1    4    1
## Hornet 4 Drive    21.4   6  258 110 3.08 3.215 19.44  1  0    3    1
## Hornet Sportabout 18.7   8  360 175 3.15 3.440 17.02  0  0    3    2
## Valiant           18.1   6  225 105 2.76 3.460 20.22  1  0    3    1
class(mtcars)
## [1] "data.frame"

The data was extracted from the 1974 Motor Trend US magazine, and comprises fuel consumption and 10 aspects of automobile design and performance for 32 automobiles (1973–74 models). You can type ??mtcars in the R console to read a description of the data.

One of the variables of interests in the data indicates the number of cylinders of the car engines (cyl). There are cars with 4, 6 or 8 cylinders.

2a | Basic bar plot

We want to summarize this data in a simple bar plot representing the number of cars in each cylinder category; i.e., how many cars have 4, 6 or 8 cylinders. However, the number of cars with 4 cylinders is not a piece of information present in the dataset, for example. To know the number it is necessary to count the rows where cyl = 4, and we are not going to do it .

ggplot2 is capable to do simple summary operations with the input variables, referred as statistical transformations. One of them is to count the occurrences of each value in a variable, which is precisely what we want to do. And geom_bar function happen to use the count statistical transformation by default on the variable mapped to the x axis.

The first thing that we are going to do is to check the class of the cyl variable:

# First we check the class of cyl
class(mtcars$cyl)
## [1] "numeric"

We see that it’s a numeric variable. In this case we want to use cyl as a categorical variable, distinguishing groups rather than indicating a value in a numerical continuous scale. For that, we need to change its class before giving it to ggplot using the as.factor() function.

# We create a new variable in the dataframe, cyl_f, that is cyl converted to factor
mtcars$cyl_f <- as.factor(mtcars$cyl)

Now we can create the bar plot:

ggplot(data = mtcars, mapping = aes(x = cyl_f)) +
  geom_bar()

Imagine that we have already a table with the number of cars with each cylinder category. If we had a precomputed data frame with cyl and number_of_cars instead, we could pass number_of_cars variable to geom_col function instead of geom_bar, that by default takes the variables mapped to x and y without transformation.

# Let's create the data frame
counts_by_cyl_data_frame <- as.data.frame(table(mtcars$cyl))
names(counts_by_cyl_data_frame) <- c("cyl", "number_of_cars")

# See the data frame
counts_by_cyl_data_frame
##   cyl number_of_cars
## 1   4             11
## 2   6              7
## 3   8             14
# New graph with geom_col
ggplot(data = counts_by_cyl_data_frame, mapping = aes(x = cyl, y = number_of_cars)) +
  geom_col()

We’ll use geom_bar if the dataset is not processed and we need to count the occurrences of a category. If we have a processed dataset with the counts, we’ll use geom_col.

2b | Groups and position

We have seen in the scatter plot example how to represent groups encoded in extra variables as colours. Say we now want to show transmission type (am) in the bar plot, in addition to the number of cylinders. We can map am to the filling colour of the bars, fill (colour aesthetic would change the edges of the rectangles). There are two types of transmission: 0 for automatic cars and 1 for manual cars.

# First we check the class of the variable
class(mtcars$am)
## [1] "numeric"
# We make am factor, and we can change the 0/1 notation for a more informative notation: automatic/manual
mtcars$am_f <- factor(mtcars$am, levels = c(0, 1), labels = c("automatic", "manual"))

# Plot
ggplot(data = mtcars, mapping = aes(x = cyl_f, fill = am_f)) +
  geom_bar()

Each geometric object in ggplot2 also has a position argument that controls how groups are arranged. In geom_bar the default position is to stack the groups. We can change it for a side-by-side position with position = "dodge".

ggplot(data = mtcars, mapping = aes(x = cyl_f, fill = am_f)) +
  geom_bar(position = "dodge")

Exercise

Update the plot above with the "fill" position adjustment instead of "dodge". What it is doing?

Answer:

Update the previous plot to group by the variable gear instead of the transmission type (am_f). gear variable is the number of forward gear: cars can have 3, 4 and 5 gears. Check if you need to transform gear to a factor.

Answer:

Example 3 | Showing the distribution of a variable: histograms

3a | Simple histogram

Now we have a new dataset called diamonds and we need to understand the distribution of some of its continuous variables. A good place to start is a histogram, that represents the number of observations in different ranges as bars.

head(diamonds)
## # A tibble: 6 × 10
##   carat cut       color clarity depth table price     x     y     z
##   <dbl> <ord>     <ord> <ord>   <dbl> <dbl> <int> <dbl> <dbl> <dbl>
## 1  0.23 Ideal     E     SI2      61.5    55   326  3.95  3.98  2.43
## 2  0.21 Premium   E     SI1      59.8    61   326  3.89  3.84  2.31
## 3  0.23 Good      E     VS1      56.9    65   327  4.05  4.07  2.31
## 4  0.29 Premium   I     VS2      62.4    58   334  4.2   4.23  2.63
## 5  0.31 Good      J     SI2      63.3    58   335  4.34  4.35  2.75
## 6  0.24 Very Good J     VVS2     62.8    57   336  3.94  3.96  2.48
class(diamonds)
## [1] "tbl_df"     "tbl"        "data.frame"

diamonds is a dataset containing the prices and other attributes of almost 54,000 diamonds. You can type ??diamonds in the R console to read a description of the data.

The function that we need is called geom_histogram() and has the statistical transformation bin by default. In this case, bin divides the variable mapped to x in ranges and counts the number of values in each bin. The number of bins is controlled with the argument binwidth. In this example we show the distribution of the weights of diamonds (carat).

ggplot(data = diamonds, mapping = aes(x = carat)) +
  geom_histogram(binwidth = 0.3)

Note that histograms deal with continuous variables while bar plots with discrete, but are sometimes confused.

3b | Multiple histograms

The diamonds dataset contains more information about diamonds, such as the quality (cut) or the color (color). To see the distribution of the weight we can try to map it to the filling cut:

ggplot(data = diamonds, mapping = aes(x = carat, fill = cut)) +
  geom_histogram(binwidth = 0.3)

Stacked histograms are difficult to interpret. We can use another position instead of the default “stacked” position. For example, using position = "dodge".

ggplot(data = diamonds, mapping = aes(x = carat, fill = cut)) +
  geom_histogram(position = "dodge", binwidth = 0.3)

But there’s even a better option. ggplot2 provides a simple way of creating small multiples or facets with the function facet_grid:

ggplot(data = diamonds, mapping = aes(x = carat, fill = cut)) +
  geom_histogram(position = "dodge", binwidth = 0.3) + 
  facet_grid(cut ~ .)

Exercise

What happens if you change the order of the facet_grid elements, i.e., (. ~ cut)?

Answer:

Which is the best subplot configuration to compare the distributions and why?

Answer:

Example 4 | Showing the distribution of a variable: boxplot

4a | Simple boxplot

Another way of showing the distribution of numerical data is by means of a boxplot. It allows to better understand the skewness through displaying the data quartiles and averages. It also shows outliers as separated dots.

The function that we are going to use is geom_boxplot(). In this example we show the distribution of the weights of diamonds (carat).

ggplot(data = diamonds, mapping = aes(y = carat)) +
  geom_boxplot()

One characteristic of boxplots is that you can show the distribution of one variable (carat) with respect to another categorical variable. For example, we can show the distribution of carat based on the color of the diamond (color).

ggplot(data = diamonds, mapping = aes(y = carat, x = color)) +
  geom_boxplot()

Exercise

Try to fill with a color the boxplot. How would you do it?

Answer:

Example 5 | Customizing a plot

5a | Modify colours

So far we have used the default colour palettes for all our representations. We may need to change them to make them accessible to colourblind people, match the colour palette of our project or give meaningful values (e.g., red for positive and blue for negative). We can control the exact mapping of a variable to an aesthetic attribute with the functions scale_*.

In the following example we manually set the color of the five type of diamond qualities. You can use other color names checking the following R color guide.

ggplot(data = diamonds, mapping = aes(x = carat, fill = cut)) +
  geom_histogram(position = "dodge", binwidth = 0.3) + 
  facet_grid(cut ~ .) +
  scale_fill_manual(values = c("sienna1", "orange", "lightseagreen", "orangered", "red4"))

Note that scale functions update both the aesthetic mappings in the plot and in the legend.

5b | Change (or add) axis, legend and plot titles

We may also need to add a title to the plot or change the axis titles. There are several options for that: * In ggplot2, axis and legend titles can be specified with name argument within a scale_* function * The title can be changed with + ggtitle("Title name") * You can also use the convenience function labs(), with fill = "" you will set a new legend title and title = "" a new title. See the working example:

# We save the common part of the plot in a variable and then we can add more components with the "+" sign
p <- ggplot(data = diamonds, mapping = aes(x = carat, fill = cut)) +
  geom_histogram(position = "dodge", binwidth = 0.3) + 
  facet_grid(cut ~ .)
  
# Option A:
p + scale_fill_manual(values = c("sienna1", "orange", "lightseagreen", "orangered", "red4"), name = "Quality") +
  scale_x_continuous(name = "Weight of the diamond") + 
  ggtitle("Diamond weight variation")

# Option B:
# p + scale_fill_manual(values = c("sienna1", "orange", "lightseagreen", "orangered", "red4")) +
#   labs(title = "Diamond weight variation", x = "Weight of the diamond", fill = "Quality")

5c | Change theme

The appearance of ggplot2 plots is controlled by the themes. The default ggplot2 theme has a gray background and “is designed to put the data forward yet make comparisons easy”. You can change the general appearance by choosing a different theme with theme_* functions. There are eight different themes available. The following example uses the “black and white” theme (theme_bw()):

ggplot(data = diamonds, mapping = aes(x = carat, fill = cut)) +
  geom_histogram(position = "dodge", binwidth = 0.3) + 
  facet_grid(cut ~ .) +
  scale_fill_manual(values = c("sienna1", "orange", "lightseagreen", "orangered", "red4"), name = "Quality") +
  scale_x_continuous(name = "Weight of the diamond") + 
  ggtitle("Diamond weight variation") +
  theme_bw()

Exercise

Using the following code, try other scale_fill_* functions in ggplot2 with pre-defined palettes, such as scale_fill_hue(), scale_fill_brewer(), scale_fill_viridis_d() (default) and scale_fill_grey(). Which palette would you use to ensure that colourblind people can distinguish the colours, scale_fill_hue() or scale_fill_viridis_d()?

Answer:

Try subtitle = "", caption ="" and tag ="" arguments from the labs() function. What are they for?

Answer:

Which theme of the eight available do you think that maximizes the data-ink ratio?

Answer:

Saving the plots

There are several ways to save a plot to a file. Here you have a couple of examples:

A. Export button from RStudio plot panel:

B. ggsave function from ggplot2 package

p <- ggplot(data = iris, mapping = aes(x = Sepal.Width, y = Sepal.Length)) + geom_point()

ggsave(filename = "plot.png", plot = p, width = 6, height = 4) # In inches by default

Plots can be saved using different image file formats. Option A gives you the format options in a drop list (image format: PNG, JPG, …), option B guesses the format from the extension (e.g. plot.png or plot.pdf).

The main formats can be classified into:

  • Raster/bitmat formats, where information is stored in pixels and have a maximum resolution.

    • PNG: extension .png, supports transparent background, good compression, doesn’t lose quality
    • JPEG: extensions .jpg and .jpeg, very good compression, used in personal photography but suffers from quality degradation with repeated modifications
    • TIFF: extensions .tif and .tiff, preferred format for professional printing

  • Vector formats, where information is encoded in geometric shapes that can be rendered at any size without losing resolution.

    • SVG: extension .svg, standard for vector graphics, requires svglite package

  • Hybrid

    • PDF: can contain both vector graphics and raster images

Exercise

Save the plot p in a raster and a vector format with the same size using ggsave() (e.g.: width = 6, height = 4). What differences do you observe when you zoom in them?

Note: svg devices require svglite R package and other system libraries (libcairo2-dev and libfontconfig1-dev). Skip the exercise if you get an error!

Answer:

Wrap up exercise

If for representing a scatter plot we use geom_point(), a bar plot geom_bar() … could you guess how to represent a line plot with ggplot2 syntax?

  • Represent how unemploy variable changes over time (date variable) from economics dataset with a line plot using ggplot2 syntax
  • Modify axis names and add a title
  • Use a theme
  • Save the plot to a file using a raster image format (png)
Answer:

The final image should look like this:

Try to reproduce a plot!

Each group has been assigned a plot. With your knowledge on ggplot2 try to write the code that reproduce the same figure.

Group Dataset Description Hint
1 Titanic Survival of passengers on the Titanic Color palette is: “#79AEB2”, “#4A6274”
2 ToothGrowth The Effect of Vitamin C on Tooth Growth in Guinea Pigs Color palette is: “#58A6A6”, “#EFA355”
3 msleep An updated and expanded version of the mammals sleep dataset. You can color in gray the NA values inside the scale_fill (na.value = “grey80”)
4 mpg Fuel economy data from 1999 and 2008 for 38 popular models of car Color palette is: “#4CC3CD”, “#FEE883”
5 midwest Midwest demographics. Two aesthetics are combined inside geom_point(), color and size.
6 diamonds Prices of 50,000 round cut diamonds The viridis palette is used.
7 HairEyeColor Hair and Eye Color of Statistics Students Color palette is: “#58A6A6”, “#EFA355”
8 infert Infertility after Spontaneous and Induced Abortion Color palette is: “#900C3F”, “#C70039”, “#FF5733”

random image random image random image random image random image random image random image random image

8. Upload your results to your GitHub

Upload this Rmd document and the figures you have generated to your GitHub repository.